I'm not sure you can't get halfway decent public schools in the cities, but they tend to be local to wealthier neighborhoods. And suburbs in the area I'm from tend to at least have apartments and townhomes, which are a nice middle ground (at least as far as saving on heating, cooling, cleaning, space, cost). The commute still sucks, of course.
In NYC at least, you don't have to live in a pricey neighborhood in order to get your kid into a good public high school. Your kid will, however, have to do well on a standardized test.
